Handsaws have been around for thousands of years. There exist Egyptian hieroglyphics depicting ancient woodworking sawing boards into pieces. Ancient bow saws have been found in Japan. The cut patterns on ancient boards may be observed sometimes to bear the unique cutting marks left by saw blades, particularly if the wood was not 'smoothed up' by some method.
Materials for saw blades have varied over the ages. There were probably bronze saws in the time before steel making technology became extensively known and industrialized within the past thousand years or so.
Sometimes cultures evolved two main types of saw teeth: the 'cross cut' saw teeth and the 'rip' saw teeth. Someone once described tree structure as being like hundreds of thousands of straws bundled together. With this in mind one can imagine the different mechanism needed to separate the straws lengthwise as opposed to cutting the straws crosswise. Thus, Cross cut saws have sawteeth that are usually shaped, often with a metal file, in such a way that they form a series of tiny knifelike edges.The wood cells (straws) are contacted by the knife-edge of the tooth and cut. Ripsaws, on the other hand, are usually shaped so that they form a series of tiny chisel-like edges. The wood cells (straw-ends) are contacted by the chisel and 'ripped' apart from the bundle of other cells. Of course either saw can be used either way, and Tage Frid has even said he thinks ripsaws are better for crosscutting!
Development of saws was also effected by the importance of wood to their society, the development of steel and other saw-making technologies, the type of power available, etc... which was in turn influenced by the environment, such as the types of ores available, the types of trees nearby and the types of wood which was in those trees. Also important were the types of jobs the saws were to perform.
Saws can also be considered 'pull cut' or 'push cut'. Ancient egyptian saws have been said to be pull cut. Modern European (and Euro influenced cultures like the United States) generally have 'push cut' handsaws. Japanese handsaws are usually pull-cut and are still used today. Many woodworkers have various theories about the advantages and disadvantages of pull vs. push, and even experts will disagree on these matters, including accuracy of cut, power available for cut, straightness of line, thinness of kerf (the slit in the wood that is made during cutting) , etc.